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A maximum entropy test for evaluating higher-order correlations in spike counts.

Onken A, Dragoi V, Obermayer K - PLoS Comput. Biol. (2012)

Bottom Line: Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small.These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1.They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.

View Article: PubMed Central - PubMed

Affiliation: Technische Universit├Ąt Berlin, Berlin, Germany. arno.onken@unige.ch

ABSTRACT
Evaluating the importance of higher-order correlations of neural spike counts has been notoriously hard. A large number of samples are typically required in order to estimate higher-order correlations and resulting information theoretic quantities. In typical electrophysiology data sets with many experimental conditions, however, the number of samples in each condition is rather small. Here we describe a method that allows to quantify evidence for higher-order correlations in exactly these cases. We construct a family of reference distributions: maximum entropy distributions, which are constrained only by marginals and by linear correlations as quantified by the Pearson correlation coefficient. We devise a Monte Carlo goodness-of-fit test, which tests--for a given divergence measure of interest--whether the experimental data lead to the rejection of the hypothesis that it was generated by one of the reference distributions. Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small. Subsequently, we apply our method to spike count data which were recorded with multielectrode arrays from the primary visual cortex of anesthetized cat during an adaptation experiment. Using mutual information as a divergence measure we find that there are spike count bin sizes at which the maximum entropy hypothesis can be rejected for a substantial number of neuronal pairs. These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1. They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.

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Illustration of the control and adaptation protocols.
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pcbi-1002539-g005: Illustration of the control and adaptation protocols.

Mentions: The new maximum entropy test was applied to neural spike trains recorded from the primary visual cortex of anesthetized cat during visual stimulation [34]. The protocols of the neurophysiological experiments are depicted in Figure 5. Drifting gratings of random orientations between and (resolution ) were presented during two conditions. In the control condition, each (test) orientation was presented for 2.5 s. In the adaptation condition, an initial block (2 min) of one grating of fixed orientation was followed by random presentations of the 8 orientations (2.5 s). Each of these (test) gratings was preceded by a 5 s presentation of the adapted grating in order to maintain the orientation effects. Simultaneous neural activity from 11 cells was recorded by multiple electrodes in V1. The resulting spike trains were binned and transformed to spike count sequences. We thereby obtained a total of 42 repetitions for each condition, orientation and non-overlapping spike train bin of varying length.


A maximum entropy test for evaluating higher-order correlations in spike counts.

Onken A, Dragoi V, Obermayer K - PLoS Comput. Biol. (2012)

Illustration of the control and adaptation protocols.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369943&req=5

pcbi-1002539-g005: Illustration of the control and adaptation protocols.
Mentions: The new maximum entropy test was applied to neural spike trains recorded from the primary visual cortex of anesthetized cat during visual stimulation [34]. The protocols of the neurophysiological experiments are depicted in Figure 5. Drifting gratings of random orientations between and (resolution ) were presented during two conditions. In the control condition, each (test) orientation was presented for 2.5 s. In the adaptation condition, an initial block (2 min) of one grating of fixed orientation was followed by random presentations of the 8 orientations (2.5 s). Each of these (test) gratings was preceded by a 5 s presentation of the adapted grating in order to maintain the orientation effects. Simultaneous neural activity from 11 cells was recorded by multiple electrodes in V1. The resulting spike trains were binned and transformed to spike count sequences. We thereby obtained a total of 42 repetitions for each condition, orientation and non-overlapping spike train bin of varying length.

Bottom Line: Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small.These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1.They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.

View Article: PubMed Central - PubMed

Affiliation: Technische Universit├Ąt Berlin, Berlin, Germany. arno.onken@unige.ch

ABSTRACT
Evaluating the importance of higher-order correlations of neural spike counts has been notoriously hard. A large number of samples are typically required in order to estimate higher-order correlations and resulting information theoretic quantities. In typical electrophysiology data sets with many experimental conditions, however, the number of samples in each condition is rather small. Here we describe a method that allows to quantify evidence for higher-order correlations in exactly these cases. We construct a family of reference distributions: maximum entropy distributions, which are constrained only by marginals and by linear correlations as quantified by the Pearson correlation coefficient. We devise a Monte Carlo goodness-of-fit test, which tests--for a given divergence measure of interest--whether the experimental data lead to the rejection of the hypothesis that it was generated by one of the reference distributions. Applying our test to artificial data shows that the effects of higher-order correlations on these divergence measures can be detected even when the number of samples is small. Subsequently, we apply our method to spike count data which were recorded with multielectrode arrays from the primary visual cortex of anesthetized cat during an adaptation experiment. Using mutual information as a divergence measure we find that there are spike count bin sizes at which the maximum entropy hypothesis can be rejected for a substantial number of neuronal pairs. These results demonstrate that higher-order correlations can matter when estimating information theoretic quantities in V1. They also show that our test is able to detect their presence in typical in-vivo data sets, where the number of samples is too small to estimate higher-order correlations directly.

Show MeSH
Related in: MedlinePlus